A p-adic monodromy theorem for curves

@misc{diao2026padic,
  title = {{A $p$-adic monodromy theorem for curves}},
  author = {Hansheng Diao and Yong Suk Moon and Zijian Yao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.11106},
  eprint = {2609.11106},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11106},
}

TY  - UNPB
TI  - A p-adic monodromy theorem for curves
AU  - Hansheng Diao
AU  - Yong Suk Moon
AU  - Zijian Yao
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.11106
UR  - https://arxiv.org/abs/2609.11106
AB  - We prove that every de Rham p-adic local system on a smooth projective curve over a p-adic field is potentially semistable; that is, it becomes semistable after pulling back along a finite cover of the curve. This establishes a relative version of the classical p-adic monodromy theorem of Berger and André--Kedlaya--Mebkhout. Along the way, we show that every p-adic differential equation near a type I\!V point on a curve becomes trivial after a finite étale extension.
ER  -